Cp = heat capacity at constant pressure, J= K kg Cv = heat capacity at constant volume, J= K kg c = concentration, mol=m E = total energy, J=m H = shape factor, = , dimensionless h = specific enthalpy, J=kg h = heat of formation, J=kg J = diffusive mass flux, kg=m s Keq = equilibrium constant k = reaction rate coefficient Le = Lewis number, dimensionless M = Mach number, dimensionless ns = tota...

For decades, researchers have worked towards developing a suitable model to represent turbulent boundary layers. Based on PIV experiments in the x − z planes of a turbulent boundary layer, Adrian et al. [1] proposed a model based on a packet of “hairpin vortices” as a primary feature in turbulence transport and production (In this paper, streamwise, spanwise and wall-normal directions are along...

Simultaneous triaxial sonic anemometer velocity measurements vertically arrayed at six levels within and above a uniform pine forest were used to examine two parameterization schemes for the triple-velocity correlation tensor employed in higher-order closure models. These parameterizations are the gradient-diffusion approximation typically used in second-order closure models, and the full budge...

Stochastic Lagrangian models for the velocity following a fluid particle are used both in studies of turbulent dispersion and in probability density function ~PDF! modeling of turbulent flows. A general linear model is examined for the important case of homogeneous turbulent shear flow, for which there are recent direct numerical simulation ~DNS! data on Lagrangian statistics. The model is defi...

Holographic PIV is used to measure the three-dimensional velocity distribution of fully developed turbulent flow within a square duct at ReH = 1.2 × 10. The data is used for mapping the structure of the filtered, three-dimensional vorticity, strain-rate and subgrid-scale (SGS) stress tensor distributions. Visualizations of iso-vorticity surfaces show structures that are only slightly elongated,...

With the rapid development of artificial intelligence, machine learning algorithms are becoming more widely applied in modification turbulence models. In this paper, with aim improving prediction accuracy Reynolds-averaged Navier–Stokes (RANS) model, a semi-implicit treatment Reynolds stress anisotropy discrepancy model is developed using higher-order tensor basis. A deep neural network constru...

Reynolds-averaged Navier-Stokes (RANS) is one of the most cost-efficient approaches to simulate wind-farm-atmosphere interactions. However, applicability RANS-based methods always limited by accuracy turbulence closure models, which introduce various uncertainties into models. In this study, we estimate model-form in RANS simulations wind farms. For purpose, compare different models a large-edd...

in classical mechanics, considering hook’s law stress is a linear function of strain. while in strain gradient theory stress is a function of strain and strain differentials. in this paper, novel formulation relating stress and strain and also new boundary conditions are derived based on minimum potential energy principle. in strain gradient theory a length coefficient parameter is defined. thi...

Turbulence equilibrium state is analyzed for the modeled Reynolds-stress transport equation, assuming most general formulation of pressure–strain correlation. In a two-dimensional mean flow at high-Reynolds number, an algebraic equation system obtained, providing anisotropies as functions model coefficients. Conversely, equations provide calibration conditions coefficients to predict specified ...

A new Reynolds stress anisotropy closure that includes nonlocal and nonequilibrium effects in turbulent flows has been obtained from a recently proposed nonlocal anisotropy formulation. This formulation is based on a new nonlocal derivation of the rapid pressurestrain correlation, which rigorously accounts for nonlocal effects on the anisotropy due to spatial variations in the mean velocity gra...